A method according to one of the aspects of the present invention, for longitudinally stretching a thermoplastic resin film by drawing the thermoplastic resin film by a pair of rolls rotating at different circumferential velocities is characterized in that an draw initiation position is set between the pair of the rolls, and that the thermoplastic resin film is longitudinally stretched, while being heated locally and rapidly by contact-free local and rapid heating device installed at the draw initiation position along the film width direction in a range from Tg of the resin film -5.degree. C. or higher to Tg +30.degree. C. or lower.